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HI6007 Statistics and Research Methods for Business Decision Making - Holmes Institute

1. Explain how statistical techniques can solve business problems

2. Identify and evaluate valid statistical techniques in a given scenario to solve business problems

3. Explain and justify the results of a statistical analysis in the context of critical reasoning for a business problem solving

4. Apply statistical knowledge to summarize data graphically and statistically, either manually or via a computer package

5. Justify and interpret statistical/analytical scenarios that best fits business solution

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Question 1

(a) Use an appropriate graphical technique to compare the amount of CO2 emissions (in millions of metric tonnes) in 2009 and 2013, broken down by the producer countries.

Solution: (b) Use an appropriate graphical technique to compare the percentage value of the amount of CO2 emissions (in %) in 2009 and 2013, broken down by the producer countries.

Solution:

b) CO2 EMISSIONS by percentage (c) Comment your observations in parts (a) and (b).

Solution:

c) in part a) China had the highest amount of CO2 emission in the year 2013 compared to other countries. United States was the leading CO2 in the year 2009 compared to other countries.

In part b) china was the leading in percentage of CO2 gas emission in 2013 while United States was the leading in percentage of gas emission in the year 2009.

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Question 2.

a. Construct a frequency distribution and a relative frequency distribution for the data.

b. Construct a cumulative frequency distribution and a cumulative relative frequency distribution for the data.

Solution: a & b

 Classes frequency Relative frequency CF CRF 35-44 3 0.075 3 0.05 45-54 4 0.1 7 0.175 55-64 9 0.225 16 0.4 65-74 18 0.45 34 0.85 75-84 4 0.1 38 0.95 85-94 1 0.025 39 0.975 95-104 1 0.025 40 1 40

c. Plot a relative frequency histogram for the data.

Solution: d. Construct an ogive for the data.

Solution:

d) Ogive graph e. What proportion of the data is less than 65?

Solution: Proportion of data less than 65 is 16/40 which is 0.4

f. What proportion of the data is more than 75? Use following class intervals to answer the above questions

Solution: Proportion of data more than 75 is 6/40 which is 0.15

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Question 3.

a. Using an appropriate graphical descriptive measure (relevant for time series data) describe the two variables.

Solution: The time series data for the rate of inflation has benn rising and falling from the year 1995 to 2015. Time series data for the rate of inflation seems to be in an uptrend since 1995. There was a decline in 2007 but it rose again until 2015

The two variables have different values for data. The rate of inflation has minimum values while All-ordinaries have high values in the data.

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b. Use an appropriate plot to investigate the relationship between RATE OF INFLATION and ALL- ORDINARIES INDEX. Briefly explain the selection of each variable on the X and Y axes and why?

Solution: x- axis is All ordinaries index and y-axis is the rate of inflation. The all ordinaries determine the rate of inflation because it is the independent variable and the dependent variable is the rate of inflation.

c. Prepare a numerical summary report about the data on the two variables by including the summary measures, mean, median, range, variance, standard deviation, and coefficient of variation, smallest and largest values, and the three quartiles, for each variable.

Solution:

Descriptive Statistics
All-ordinaries

Sample Size, n: 21
Mean: 3982.733
Median: 4127.6
Midrange: 4169.2
RMS: 4161.737
Variance, s^2: 1.530783e+6
St. Dev., s: 1237.248
Mean Abs Dev: 1058.984
Range: 4336.8
Coeff. Of Var. 31.07%

Minimum: 2000.8
1st Quartile: 3032
2nd Quartile: 4127.6
3rd Quartile: 4933.5
Maximum: 6337.6

Sum: 83637.4
Sum Sq: 3.637211e+8

Descriptive Statistics
Rate of Inflation

Sample Size, n: 21
Mean: 2.690476
Median: 2.5
Midrange: 3.1
RMS: 2.931682
Variance, s^2: 1.423905
St. Dev., s: 1.193275
Mean Abs Dev: 0.8081633
Range: 5.6
Coeff. Of Var. 44.35%

Minimum: 0.3
1st Quartile: 2.4
2nd Quartile: 2.5
3rd Quartile: 2.9
Maximum: 5.9

Sum: 56.5
Sum Sq: 180.49

d. Calculate the coefficient of correlation (r) between RATE OF INFLATION and ALL-ORDINARIES INDEX. Then, interpret it.

Solution: Co-efficient of correlation

 all ordinaries rate of inflation all ordinaries 1 rate of inflation 0.038875116 1

The correlation co-efficient between the two variables is 0.038 which is positive. This shows that the relationship is weak since it is less than 0.5.

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e. Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model.

Solution: Linear regression

Regression analysis show the relationship between variables (Patten & Newhart, 2017).

Sample size, n: 21
Degrees of freedom: 19

Correlation Results:
Correlation coeff, r: 0.0388751
Critical r: ±0.4328579
P-value (two-tailed): 0.86713

Regression Results:
Y= b0 + b1x:
Y Intercept, b0: 2.54115
Slope, b1: 0.0000375

Total Variation: 28.4781
Explained Variation: 0.0430382
Unexplained Variation: 28.43506
Standard Error: 1.223349
Coeff of Det, R^2: 0.0015113

Linear equation
The Linear equation is given byY= b0 + b1x:
Y Intercept, b0: 2.54115
Slope, b1: 0.0000375

The Linear equation is Y= 2.54+ 0.0000375x

f. Determine the coefficient of determination R2 and interpret it.

Solution: Co-efficient of determination

The co-efficient of determination is 0.0015 meaning that 0.15% of the variation in the rate of inflation can be explained by the independent variable All-ordinaries.

g. Test the significance of the relationship at the 5% significance level.

Solution: P-value 0.867 >0.05 means that the model is insignificant for predicting the relationship between the variables.

h. What is the value of the standard error of the estimate (se). Then, comment on the fitness of the linear regression model?

Solution: Standard error
Standard Error: 1.223349
The linear regression is a weak fit for the prediction.

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